McLachlan G., Basford K. Mixture Models: Inference and Application to Clustering

New York: Marcel Dekker, 1988. — 273 p.The purpose of this book is to highlight the important role of finite mixture distributions in modeling heterogeneous data, with the focus on applications in the field of cluster analysis. With the increasing interest on a model-based approach to clustering, the use of finite mixture models for this purpose has been the subject of close scrutiny recently. The practical applications of mixture models are presented against the background of the existing literature for inference undertaken in a finite mixture framework. Attention is concentrated on the fitting of mixture models by a likelihood-based approach, using maximum likelihood where appropriate.
This approach would appear in general to be superior to other methods of fitting mixture models, and the EM algorithm provides a convenient way for the iterative computation of solutions of the likelihood equation. However, it has only been in relatively recent times with the wide availability of high-speed computers that serious consideration has been given to the fitting of mixture models to data of more than one dimension.